Answers
Since we have a right triangle, we can relate the angle 28 with x and side 34 by meand of the sine function, that is,
[tex]\sin 28=\frac{34}{x}[/tex]where x is the hypotenuse. By moving x to the left hand side, we have
[tex]x\cdot\sin 28=34[/tex]and by moving sin28 to the right hand side, we get
[tex]x=\frac{34}{\sin 28}[/tex]since sin28=0.4694, we have
[tex]x=\frac{34}{0.4694}[/tex]then, x is given by
[tex]x=72.42[/tex]by rounding down, the answer is option D: x=72.4
Related Questions
In ACDE, m/C= (5x+18), m/D= (3x+2), and m/B= (2+16)°.
Answers
Angle (D) = m(D) = 50°, CDE provides the following: 3. angles
m=C=(5x+18), m=D=(3x+2), and m=E=(x+16)°.The total of the angles in a triangle is 180°What are angles?An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.CDE provides the following: 3. angles
m<C=(5x+18),m<D=(3x+2), andm<E=(x+16)degree.The total of the angles in a triangle is 180 degrees, so:
"mC + mD + mE = 180°"(5x+18)° + (3x+2)° + (x+16)° = 180°5x + 18 + 3x + 2 + x + 16 = 180°5x + 3x + x + 18 + 2 + 16 = 180°9x +36= 180°From both sides, deduct 36 as follows:
9x + 36 - 36 = 180° - 36°9x = 144°x = 144°/9x = 16From the aforementioned query, we are requested to determine:
angular D (m<D)Hence:
m∠D=(3x+2)°m∠D=( 3 × 16 + 2)°m∠D=(48 + 2)°m∠D= 50°Therefore, angle (D) = m(D) = 50°, CDE provides the following: 3. angles
m=C=(5x+18), m=D=(3x+2), and m=E=(x+16)°.The total of the angles in a triangle is 180°To learn more about angles, refer to:
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please show work on how to get the points we graph
Answers
Answer:
Graphing the inequalities, we have;
Explanation:
Given the system of quadratic inequalities;
[tex]\begin{cases}y<-x^2-x+8 \\ y>x^2+2\end{cases}[/tex]Graphing the quadratic inequalities;
for the first quadratic inequality;
[tex]\begin{gathered} y<-x^2-x+8 \\ at\text{ x=0} \\ y<8 \\ (0,8) \\ at\text{ x=-0.5} \\ y<-(-0.5)^2-(-0.5)+8 \\ y<8.25 \\ (-0.5,8.25) \\ at\text{ x=-2} \\ y<-(-2)^2-(-2)+8 \\ y<-4+2+8 \\ y<6 \\ (-2,6) \\ at\text{ x=}2 \\ y<-(2)^2-(2)+8 \\ y<-4^{}-2+8 \\ y<2 \\ (2,2) \end{gathered}[/tex]For the second quadratic inequality;
[tex]\begin{gathered} y>x^2+2 \\ at\text{ x=0} \\ y>2 \\ at\text{ x=2} \\ y>(2)^2+2 \\ y>6 \\ (2,6) \\ at\text{ x=-2} \\ y>(-2)^2+2 \\ y>6 \\ (-2,6) \end{gathered}[/tex]Graphing the two inequalities using the points derived above.
Note that both inequalities would be dashed lines because of the inequality sign, and the shaded part will be according to the sign.
Graphing the inequalities, we have;
How many times in the parabola does a line intersect?
Answers
The line can intersect the parabola at one or two points.
See the example below.
The black line intersects the parabola at (1, -1)
The blue line intersects the parabola at two points: (0, 0) and (4, 8).
I just finished my other 2 questions and I need help with this one now, I don't understand the letters really. please help
Answers
So, c(x) = 8.25x + 1500
the marginal cost doubles so, (8.25 x) will be 2 * (8.25x )
And the fixed cost decreased by 30%
so, 1500 will be (1 - 30%) of 1500
so, (1 - 30%) of 1500 = 70% of 1500 = 0.7 * 1500 = 1050
So, k(x) = 2 * (8.25x) + 1050
K(x) = 16.5 x + 1050
Three-inch pieces are repeatedly cut from a 42-inch string. The length of the string after x cuts is given by y = 42 – 3x. Find and interpret the x- and y-intercepts.
Answers
Answer:
y-intercept: 42
x-intercept: 14
Step-by-step explanation:
The y-intercept can be found with the given equation:
y = 42 - 3x
Either Let x = 0 to find the y-intercept. OR,
rearrange the equation to y=mx+b to see the y-intercept, which is b in the equation.
y = 3(0) + 42
y = 42
The y-intercept is 42 and this means that the original, uncut length of the string (zero cuts) is 42.
To find the x-intercept, let y = 0.
y = 42 - 3x
0 = 42 - 3x
Add 3x to both sides.
3x = 42
Divide by 3.
x = 42/3
x = 14
An x-intercept of 14, means that at 14 cuts there will be no more string left. The length of the string is now 0.
identify the constant of proportionality in the following questions. 1) y= 2x + 32) y= -3x - 4
Answers
Answer:
0. k=2
,1. k=-3
Explanation:
The constant of proportionality is the number that is beside the variable x in both equations.
(1)For the equation:
[tex]y=2x+3[/tex]The constant of proportionality is 2.
(2)For the equation:
[tex]y=-3x-4[/tex]The constant of proportionality is -3.
HELP PLEASEEEEE!!!!!!
Answers
The rational number is -91/100 or -0.91.
What is Rational number?Any number of the form p/q, where p and q are integers and q is not equal to 0, is a rational number. The letter q stands for the set of rational numbers.
The word "ratio" is where the word "rational" first appeared. Rational numbers are therefore closely tied to the idea of fractions, which stand for ratios. In other terms, a number is a rational number if it can be written as a fraction in which the numerator and denominator are both integers.
Given:
We have to find the rational number between -1/3 and -1/2
Tale LCM for 3 and 2 = 6
-1/3 x 2/2 and -1/2 x 3/3
-2/6 and -3/6
Now, multiply 10
-2/6 x 10/10 and -3/6 x 10/10
-20/60 and -30/60.
Hence, the rational number is -21/60.
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determine whether or not each spaceship trip below has the same speed as Saiges spaceship
Answers
1) Since Saige's spaceship makes 588 km in 60 seconds we can find its velocity:
[tex]\begin{gathered} V=\frac{d}{t} \\ V=\frac{588}{60}=\frac{49}{5}\text{ =9.8 km /s} \\ \\ V_2=\frac{441}{45}=\frac{49}{5} \\ V_3=\frac{215}{25}=\frac{43}{5} \\ V_4=\frac{649}{110}=\frac{59}{10} \end{gathered}[/tex]2) After simplifying we can state:
441/45 = has the same speed as Saige's spaceship
215/25 = does not have the same speed as Saige's space
649/110 =does not have the same speed as Saige's space
If the vertices of three squares are connected to form a right triangle, the sum of the areas of the two smaller squares is the same as the area of the largest square. Based on this statement and the model below, what is the area of square B? (Figure is not drawn to scale.) B 8 m 2 289 m
Answers
One square has area 289 square meters, and the other has area
[tex]8m\times8m=64m^2[/tex]Then, since the sum of the two areas of the smaller squares is equal to the area of the big square, we have
[tex]\begin{gathered} B+64m^2=289m^2 \\ B=289m^2-64m^2 \\ B=225m^2 \end{gathered}[/tex]How do the graphs of transformations compared to the graph of the parent function. Need the answer to this
Answers
• A ,Reflection
,• A ,Vertical Shift 4 units down
1) Considering the parent function, i.e. the simplest form of a family of functions, in this case, to be:
[tex]f(x)=x^4[/tex]2) Then we can state that this transformed function:
[tex]g(x)=-x^4-8[/tex]We can see the following transformations:
• A ,Reflection,, pointed out by the negative coefficient
,• A ,Vertical Shift 4 units down
As we can see below, to better grasp it:
3 hours 6 minutes 45 seconds Plus 8 hours 55 minutes 20 seconds
Answers
12h 2 minutes and 5 seconds
1) Adding 3 hours 6 minutes and 45 seconds to 8 hours 55 minutes and 20 seconds we can write like this:
2) Every time we hit 60'' (seconds) we add to its neighbor then we can find the following sum.
1h ----60'
1 minute ----60''
3) Then the sum of those is equal to 12h 2 minutes and 5 seconds
A committee must be formed with 4 teachers and 4 students. If there are 7 teachers to choose from, and 9 students, how many different ways could the committee be made?
Answers
ANSWER
4,410
EXPLANATION
The number of ways we can choose 4 teachers from 7 teachers is,
[tex]_7C_4=\frac{7!}{(7-4)!\times4!}=\frac{7\times6\times5\times4!}{3!\times4!}=\frac{7\times6\times5}{3\times2}=\frac{7\times6\times5}{6}=7\times5=35[/tex]There are 35 ways of choosing 4 teachers out of 7.
And the number of ways we can choose 4 students from 9 students is,
[tex]\begin{gathered} _9C_4=\frac{9!}{(9-4)!\times4!}=\frac{9\times8\times7\times6\times5\times4!}{5!\times4!}=\frac{9\times8\times7\times6\times5}{5\times4\times3\times2} \\ _9C_4=\frac{9\times8\times7}{4}=\frac{9\times(2\times4)\times7}{4}=9\times7\times2=126 \end{gathered}[/tex]There are 126 ways of choosing 4 students out of 9.
The committee is formed by 4 teachers and 4 students. The number of ways it can be made is,
[tex]_7C_4\times_9C_4=35\times126=4,410[/tex]Hence, there are 4,410 ways to choose 4 students and 4 teachers out of 9 students and 7 teachers.
Which of the following are solutions to the inequality below? Select all that apply.
Answers
Step-by-step explanation:
1.12+8×10<66
12+80<66
92<66
2.12+8×3<66
12+24<66
36<66
3.12+8×8<66
12+64<66
76<66
4.12+8×4<66
12+32<66
44<66
therfore the answer is 2 and 4
Find the equation of the line parallel to the line y=-1, going through point (-5,4)
Answers
In this problem, want to find the equation of a line that will be parallel to a given function through a point.
Recall that parallel lines have the same slope.
We are given the line
[tex]y=-1[/tex]and the point
[tex](-5,4)[/tex]Notice that the equations is technically in slope-intercept form, by the value of the slope will be 0:
[tex]y=0x-1[/tex]Therefore, the slope of the line through (-5,4) will also be zero. We can use that information to find the equation.
Using the form
[tex]y=mx+b[/tex]we can substitute the point and the slope to solve for b:
[tex]\begin{gathered} 4=0(-5)+b \\ \\ 4=b \end{gathered}[/tex]So, the equation of our line is:
[tex]y=0x+4\text{ or }\boxed{y=4}[/tex]X 즈 - + 3 = 15 -4someone help me confused
Answers
First we have to transfer the number 3 the other side of equal sign as follows,
[tex]\begin{gathered} \frac{x}{-4}=15-3 \\ \frac{x}{-4}=12 \end{gathered}[/tex]Now, we need to transfer (-4) to the other side of the equal side by multiplying with the number 12.
[tex]\begin{gathered} \frac{x}{-4}=12 \\ x=12\ast(-4) \\ x=-48 \end{gathered}[/tex]Thus, the answer of the x is (-48).
Red Tickets: 50 tickets for $37.50A sign at the fair advertises ticket prices for the carnival games,Blue Tickets: 20 tickets for $16.00Yellow Tickets: 5 tickets for $5.00Find the price per ticket for each:Red ticketBlue Ticket:Yellow Ticket:How much would 40 red tickets costs?123456 7 10
Answers
The price per ticket can be calculated as follows;
[tex]\begin{gathered} \operatorname{Re}d=\frac{\text{Price}}{No\text{ of tickets}} \\ \operatorname{Re}d=\frac{37.50}{50} \\ \operatorname{Re}d=0.75 \\ \text{Blue}=\frac{16}{20} \\ \text{Blue}=0.8 \\ \text{Yellow}=\frac{5}{5} \\ \text{Yellow}=1.00 \end{gathered}[/tex]The price per ticket for each is given as;
Red tickets = $0.75
Blue tickets = $0.80
Yellow tickets = $1.00
Therefore, 40 red tickets would cost
40 Red = 0.75 x 40
40 Red tickets = $30.00
A bag contains 3 gold marbles, 10 silver marbles, and 23 black marbles. You randomly select one marblefrom the bag. What is the probability that you select a gold marble? Write your answer as a reduced fractionPlgold marble)
Answers
ANSWER
P(gold marble) = 1/12
EXPLANATION
In total, there are:
[tex]3+10+23=36[/tex]36 marbles in the bag, where only 3 are gold marbles.
The probability is:
[tex]P(\text{event)}=\frac{\#\text{times the event can happen}}{\#\text{posible outcomes}}[/tex]In this case, the number of posible outcomes is 36, because there are 36 marbles in the bag. The number of times the event can happen is 3, because there are 3 gold marbles:
[tex]P(\text{gold marble)}=\frac{3}{36}=\frac{1}{12}[/tex]A line passes through the point −6, 3 and has a slope of 32 .Write an equation in slope-intercept form for this line.
Answers
The equation of the straight line that passes through the point (-6, 3) will be y = 32x + 195.
What is the slope - intercept form of the equation of a straight line?
The slope - intercept form of the equation of a straight line is -
y = mx + c
Where -
[m] is the slope of the line.
[c] is the y - intercept.
Given is a line that passes through the point (−6, 3) and has a slope of 32.
We know that the slope - intercept form can be written as -
y = mx + c
Now, the slope of the line = [m] = 32
Since, the line passes through the point (-6, 3), we can write -
3 = 32 x -6 + c
3 = -192 + c
c = 3 + 192
c = 195
So, the equation of the straight line that passes through the point (-6, 3) will be -
y = 32x + 195
Therefore, the equation of the straight line that passes through the point (-6, 3) will be y = 32x + 195
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Monica did an experiment to compare two methods of warming an object. The results are shown in thetable below. Which statement best describes her results?
Answers
The correct answer is,
The temperature using method 2 changed exponentially.
Solve each system of equations algebraically.[tex]y = {x}^{2} + 4 \\ y = 2x + 7[/tex]
Answers
From the problem, we two equations :
[tex]\begin{gathered} y=x^2+4 \\ y=2x+7 \end{gathered}[/tex]Since both equation are defined as y in terms of x, we can equate both equations.
[tex]\begin{gathered} y=y \\ x^2+4=2x+7^{} \end{gathered}[/tex]Simplify and solve for x :
[tex]\begin{gathered} x^2+4=2x+7 \\ x^2-2x+4-7=0 \\ x^2-2x-3=0 \end{gathered}[/tex]Factor completely :
[tex]\begin{gathered} x^2-2x-3=0 \\ (x-3)(x+1)=0 \end{gathered}[/tex]Equate both factors to 0 then solve for x :
x - 3 = 0
x = 3
x + 1 = 0
x = -1
We have two values of x, x = 3 and -1
Substitute x = 3 and -1 to any of the equation, let's say equation 2 :
For x = 3
y = 2x + 7
y = 2(3) + 7
y = 6 + 7
y = 13
One solution is (3, 13)
For x = -1
y = 2x + 7
y = 2(-1) + 7
y = -2 + 7
y = 5
The other solution is (-1, 5)
The answers are (3, 13) and (-1, 5)
use the figure to the right to find the value of PT
Answers
the figure show, the length between P and T and the length between T and Q, are equal.
so we can say PT=TQ
PT= 3x+2 and TQ=5x-6
so we can replace:
3x+2=5x-6
now we solve
2+6=5x-3x
8=2x
8/2=x=4
and finally, to find PT we replace x by 4
PT=3*4+2=14
So the answer is: PT=14
You are looking for summer work to help pay for college expenses. Your neighbor is interested in hiring you to do yard work and other odd jobs. You tell them that you can start right away and will work all day July 1 for 3 cents. This gets your neighbor's attention, but they is wondering if there is a catch. You tell them that you will work July 2 for 9 cents, July 3 for 27 cents, July 4 for 81 cents, and so on for every day in the month of July. Which equation will help you determine how much money you will make in July?
Answers
Answer:
y=3^x
Explanation:
The expected payments (in cents) beginning from July 1 are given below:
[tex]3,9,27,81,\cdots[/tex]Observing the payments for each subsequent day, we see that the payment for the previous day was multiplied by 3.
We can rewrite the payment as a power of 3 as follows:
[tex]3^1,3^2,3^3,3^4,\cdots[/tex]Therefore, the equation will help you determine how much money you will make in July will be:
[tex]y=3^x[/tex]The first option is correct.
find the size of each interior angle of a regular hexagon
Answers
Answer:
Each interior angle = 180° -60° = 120°
Step-by-step explanation: We know that the three angles in a triangle, add up to 180°, and all the three angles are 60° in an equilateral triangle. The total number of angles of an enclosed space is 180° (n-2) where in is the number of sides.
A hexagon has six sides, so: s= 180° (6-2)
s= 180° x 4
s= 720°
now since in a regular shape, each interior angle is equal. We just divide the total interior angle with a number of sides
6.
720° divided by 6 is equal to 120°
As the table shows, projections indicate that the percent of adults with diabetes could dramatically increase.Answer parts a. through c.c. In what year does this model predict the percent to be 27.96%(round to the closest year)
Answers
b. You have to consider year 2000 as the initial year, i.e. as x=0.
To predict the percent of adults with diabetes in 2014, first, you have to calculate the difference between this year and the initial year to determine which value of x you need to use:
[tex]x=2014-2000=\text{ }14[/tex]The value of x you have to use is x=14
Replace this value into the linear model calculated in item a to predict the percentage of adults with diabetes (y)
[tex]\begin{gathered} y=0.508x+10.692 \\ y=0.508\cdot14+10.692 \\ y=7.112+10.692 \\ y=17.804 \end{gathered}[/tex]In the year 2014, the predicted percentage of adults with diabetes is 17.8%
c. You have to determine the year in which the model predicts the percent to be 27.96%.
To determine this year, you have to equal the linear model to 27.96% and calculate for x:
[tex]\begin{gathered} y=0.508x+10.692 \\ 27.96=0.508x+10.692 \end{gathered}[/tex]-Subtract 10.692 from both sides of the equal sign
[tex]\begin{gathered} 27.96-10.692=0.508x+10.692-10.692 \\ 17.268=0.508x \end{gathered}[/tex]-Divide both sides by 0.508
[tex]\begin{gathered} \frac{17.268}{0.508}=\frac{0.508x}{0.508} \\ 33.99=x \\ x\approx34 \end{gathered}[/tex]Next, add x=34 to the initial year:
[tex]2000+34=2034[/tex]The model predicts the percentage to be 27.96% for the year 2034
6. sin D - Ог F 25 ot E 7. cos F. 24 8. sin F Nodule 13
Answers
In the given triangle :
FD = 25, FE = 7, DE = 24
SinD
From the trignometric ratio of sin: It express as the ratio of measurement of the side opposite to the angle to the measurement of hypotenuse of triangle DEF,
So, the SinD is express as :
[tex]\begin{gathered} \sin D=\frac{Opposite\text{ side}}{Hypotenuse} \\ \sin D=\frac{FE}{DF} \\ \sin D=\frac{7}{25} \end{gathered}[/tex]sin D = 7/25
cos F
From the trignometric ratio of cos : It expresses as the ratio of measurement of the side adjacent to the angle and to the hypotenuse of the triangle
So, the Cos F is express as :
[tex]\begin{gathered} \cos F=\frac{Adjacent\text{ side}}{Hypotenuse} \\ \cos F=\frac{FE}{DF} \\ \cos F=\frac{7}{25} \end{gathered}[/tex]cos F = 7/25
Sin F
From the trignometric ratio of sin: It express as the ratio of measurement of the side opposite to the angle to the measurement of hypotenuse of triangle DEF,
so, Sin F is express as :
[tex]\begin{gathered} \sin F=\frac{Opposite\text{ side}}{Hypotenuse} \\ \sin F=\frac{DE}{DF} \\ \sin F=\frac{24}{25} \end{gathered}[/tex]sin F = 24/25
Answer :
sin D = 7/25
cos F = 7/25
sin F = 24/25
What’s the correct answer answer asap for brainlist please
Answers
Answer:
c. you can't be feeling alive with wearing,weakness of body and mind.
Over the next 10 years, town A is expecting to gain 1000 people each year. During the same time period, the population of town B is expected to increase by 5% each year. Both town A and town B currently have populations of 10,000 people. The table below shows the expected population of each town for the next three years.Which number of years is the best approximation of the time until town A and town B once again have the same population?
Answers
From the given figure we can see
The population in town A is increased by a constant rate because
[tex]\begin{gathered} 11000-10000=1000 \\ 12000-11000=1000 \\ 13000-12000=1000 \end{gathered}[/tex]Since the difference between every 2 consecutive terms is the same, then
The rate of increase of population is constant and = 1000 people per year
The form of the linear equation is
[tex]y=mx+b[/tex]m = the rate of change
b is the initial amount
Then from the information given in the table
m = 1000
b = 10,000
Then the equation of town A is
[tex]y=1000t+10000[/tex]Fro town B
[tex]\begin{gathered} R=\frac{10500}{10000}=1.05 \\ R=\frac{11025}{10500}=1.05 \\ R=\frac{11576}{11025}=1.05 \end{gathered}[/tex]Then the rate of increase of town by is exponentially
The form of the exponential equation is
[tex]y=a(R)^t[/tex]a is the initial amount
R is the factor of growth
t is the time
Since R = 1.05
Since a = 10000, then
The equation of the population of town B is
[tex]y=10000(1.05)^t[/tex]We need to find t which makes the population equal in A and B
Then we will equate the right sides of both equations
[tex]10000+1000t=10000(1.05)^t[/tex]Let us use t = 4, 5, 6, .... until the 2 sides become equal
[tex]\begin{gathered} 10000+1000(4)=14000 \\ 10000(1.05)^4=12155 \end{gathered}[/tex][tex]\begin{gathered} 10000+1000(5)=15000 \\ 10000(1.05)^5=12763 \end{gathered}[/tex][tex]\begin{gathered} 10000+1000(6)=16000 \\ 1000(1.05)^6=13400 \end{gathered}[/tex][tex]\begin{gathered} 10000+1000(30)=40000 \\ 10000(1.05)^{30}=43219 \end{gathered}[/tex]Since 43219 approximated to ten thousand will be 40000, then
A and B will have the same amount of population in the year 30
The answer is year 30
Expected FrequencyA fair five sided spinner is spun 40 times.a) How many times would it be expectedto land on red?P(Red) = 15It would be expected to land on redItimes.1-5Hint:Set up and solve a proportion.
Answers
It can be observed that sppiner is spun 40 times. So proabaility for red colour must include 40 in denominator. The fraction 1/5 has 5 in denominator which be change to 40 by multiplication of 8 to numerator and denominator.
[tex]\frac{1}{5}\cdot\frac{8}{8}=\frac{8}{40}[/tex]So, it is expected to land 8 times on the red colour.
So answer is,
[tex]\frac{1}{5}=\frac{8}{40}[/tex]and It would be expected to land on red 8 times.
solve using the quadratic formulax^2+2x-17=0
Answers
Write an equation and solve to find the value of your variable. 7.3 less than -2 times a number is the same as 16 1/2. n=?
Answers
The equation is -2n - 7.3 = 16 1/2
The value of the variable n = -11.9
STEP - BY - STEP EXPLANATION
What to find?
• Write the equation of the given statement.
,• The value of n.
Given:
find the value of your variable. 7.3 less than -2 times a number is the same as 16 1/2. n=?
To solve follow the steps below:
Step 1
Translate the given statement into equation.
Let n be the number.
-2n - 7.3 = 16 1/2
Step 2
Convert 16 1/2 to decimal.
-2n - 7.3 = 16.5
Step 3
Add 7.3 to both-side of the equation.
-2n = 16.5 + 7.3
Step 4
Simplify the right-hand side of the equation.
-2n =23.8
Step 5
Divide both-side of the equation by -2.
[tex]\frac{\cancel{-2}n}{\cancel{-2}}=\frac{23.8}{-2}[/tex]n = -11.9
Therefore, the value of the variable n = -11.9
